President Barack Obama has continued to recalibrate his promise that "you'll be able to keep your health-care plan" under the Affordable Care Act, adding new language to those oft-repeated words and arguing that those who are losing their insurance will end up with better coverage.

The altered phrasing comes amid criticism that Mr. Obama didn't properly characterize the law since thousands of Americans are receiving notices that their health insurance has been canceled. The administration has worked to explain...